Please use this identifier to cite or link to this item: http://hdl.handle.net/1783.1/55127

Calibration of high-dimensional precision matrices under quadratic loss

Authors Zhang, M.
Rubio, F.
Palomar, D.P. View this author's profile
Issue Date 2012
Source ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings , 2012, p. 3365-3368
Summary When the observation dimension is of the same order of magnitude as the number of samples, the conventional estimators of covariance matrix and its inverse perform poorly. In order to obtain well-behaved estimators in high-dimensional settings, we consider a general class of estimators of covariance matrices and precision matrices (i.e. the inverse covariance matrix) based on weighted sampling and linear shrinkage. The estimation error is measured in terms of the matrix quadratic loss, and the latter is used to calibrate the set of parameters defining our proposed estimator. In an asymptotic setting where the observation dimension is of the same order of magnitude as the number of samples, we provide an estimator of the precision matrix that is as good as the oracle estimator. Our research is based on recent contributions in the field of random matrix theory and Monte-Carlo simulations show the advantage of our precision matrix estimator in finite sample size settings. © 2012 IEEE.
ISSN 1520-6149
ISBN 9781467300469
Language English
Format Conference paper
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